A method for characterizing grinding tooth face waviness

Abstract

The application relates to the technical field of gear machining, and discloses a method for characterizing the corrugation of a ground tooth surface. The method calculates the normal distance between discrete points on a theoretical tooth surface and a grinding wheel profile at each meshing point position, and continuously updates and retains the minimum normal distance between each discrete point and the grinding wheel profile; the discrete points are mapped into a three-dimensional coordinate system with the meshing line as the horizontal coordinate, the tooth width position as the vertical coordinate and the normal distance as the height coordinate, and are fitted into a three-dimensional curved surface; two-dimensional Fourier transformation is carried out on the fitted curved surface to obtain a corrugation curved surface which can be characterized by two-dimensional trigonometric functions. The method solves the actual tooth surface through the meshing principle, obtains the tooth surface corrugation topography by solving the normal distance between the actual tooth surface and the theoretical tooth surface, and obtains the characterization function of the tooth surface corrugation by using two-dimensional Fourier transformation on the tooth surface. The corrugation characterized by the method is consistent with the tooth surface corrugation generated in actual machining, and the method meets the detection requirement of the tooth surface corrugation in gear machining.

Description

Technical Field

[0001] This invention relates to the field of gear machining technology, specifically a method for characterizing the waviness of ground tooth surfaces. Background Technology

[0002] With the rapid development of the new energy vehicle industry, its advantages of higher energy efficiency and simpler structure compared with traditional fuel vehicles have been widely recognized. However, the gear speed in the transmission system of new energy vehicles can reach up to 20,000 rpm. The significantly increased speed will cause stronger vibration and impact, which will directly lead to a significant increase in gear meshing noise, becoming one of the key issues restricting the improvement of NVH (noise, vibration and harshness) performance of new energy vehicles.

[0003] Studies have shown that tooth surface waviness is a core factor affecting gear meshing noise. During gear transmission, tooth surface waviness alters the actual meshing trajectory, leading to periodic fluctuations in the transmission error of the gear pair. The dynamic changes in transmission error are one of the main excitation sources of gear meshing noise. In traditional gear manufacturing processes, tooth surface waviness is typically measured using a profiler to collect tooth surface data, followed by FFT to separate periodic deviations and obtain waviness data. However, this method is time-consuming and costly, allowing only sampling inspections and preventing the measurement of tooth surface waviness on every finished gear. This makes it difficult to meet the high-precision manufacturing requirements of high-speed, low-noise gears for new energy vehicles. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for characterizing the waviness of ground tooth surfaces, which has the advantage of meeting the requirements for tooth surface waviness detection in gear processing and solves the aforementioned technical problems.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for characterizing the waviness of ground tooth surfaces, comprising the following steps: S1: Construct a continuous generating grinding mathematical model that includes vibration parameters, and solve to determine the meshing point between the gear and the worm wheel; S2: Establish the equation of the theoretical gear tooth surface and discretize the theoretical tooth surface to obtain discrete points uniformly distributed on the theoretical tooth surface; S3: Calculate the normal distance between discrete points on the theoretical tooth surface and the grinding wheel profile at each meshing point position, and continuously update it, retaining the minimum normal distance between each discrete point and the grinding wheel profile. Map the above discrete points to a three-dimensional coordinate system with the meshing line as the abscissa, the tooth width position as the ordinate, and the normal distance as the height coordinate, and fit it into a three-dimensional surface; S4: Perform a two-dimensional Fourier transform on the fitted surface to obtain a waviness surface that can be characterized by two-dimensional trigonometric functions.

[0006] As a preferred technical solution of the present invention, the determination of the meshing point between the gear and the worm grinding wheel in S1 is specifically based on the meshing principle of continuous gear generating grinding, combined with the dynamic relative motion relationship between the worm grinding wheel and the gear to be processed during the grinding process, and based on the fact that the product of the relative velocity at the meshing point and the normal vector of the common tangent plane is zero, a numerical iterative algorithm is used to solve the problem and obtain the gear tooth surface enveloped by the meshing point.

[0007] As a preferred embodiment of the present invention, the specific expression for establishing the equation of the theoretical gear tooth surface in step S2 is as follows: in, Indicates tooth surface The theoretical tooth surface equation, ,when The time indicates the left tooth surface. The time indicates the right tooth surface. Represents the cosine function. Represents the sine function. Indicates the pitch. Indicates the development angle. This represents the dynamic initial angle of the involute. This indicates the angle of rotation of the tooth surface when the grinding wheel, worm gear, and gear tooth surfaces are correctly meshed before machining. This represents the radius of the base circle.

[0008] As a preferred embodiment of the present invention, the radius of the base circle The specific expression is as follows: in, Represents the tangent function. Represents the cosine function. Represents the sine function. Indicates the normal pressure angle. Indicates the nominal helix angle of the gear. Indicates the nominal cone angle of the gear. Let be the pitch circle radius of the gear.

[0009] As a preferred technical solution of the present invention, the dynamic initial angle of the involute The specific expression is as follows: in, Represents the tangent function. Represents the cosine function. Represents the sine function. Indicates the number of teeth on a gear. Indicates the end face pressure angle. This indicates the length of axial movement of the involute curve on the end face of the gear.

[0010] As a preferred embodiment of the present invention, step S4 specifically involves sampling along the waviness x and y directions and performing Fourier decomposition, as shown in the following specific expressions: in, Represents a waviness surface. These represent the x-direction and the y-direction, respectively.

[0011] Compared with the prior art, the present invention provides a method for characterizing the waviness of ground tooth surfaces, which has the following beneficial effects: This invention introduces machine tool spindle vibration displacement parameters to establish a mathematical model for continuous generating grinding of variable-thickness gears using a worm wheel that incorporates vibration. By solving for the normal distance between the theoretical tooth surface and the profile at each instantaneous position of the worm wheel, the tooth surface waviness is obtained. A two-dimensional Fourier transform is applied to this waviness to obtain its characterization function. The waviness characterized by this method closely matches the tooth surface waviness generated in actual machining, thus meeting the requirements for tooth surface waviness detection in gear machining. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the outline structure of the dressing wheel of the present invention; Figure 2 This is a schematic diagram of the dressing wheel envelope worm gear grinding wheel structure of the present invention; Figure 3 This is a schematic diagram of the worm gear grinding wheel envelope thickening gear structure of the present invention; Figure 4 This is a schematic diagram of the theoretical tooth surface mesh discretization structure of the present invention; Figure 5 This is a schematic diagram illustrating the calculation process of the normal distance between the theoretical tooth surface and the actual tooth surface in this invention. Figure 6 This is a schematic diagram of the tooth surface waviness structure of the present invention; Figure 7 This is a schematic diagram of the two-dimensional Fourier transform sampling direction structure of the present invention; Figure 8 This is a schematic diagram of the ripple structure represented by the two-dimensional trigonometric functions of the present invention; Figure 9 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] Please see Figures 1-9 A method for characterizing the waviness of ground tooth surfaces includes the following steps: S1: Construct a continuous generating grinding mathematical model that includes vibration parameters, and solve to determine the meshing point between the gear and the worm wheel; The profile of the dressing wheel is consistent with the normal profile of the feed rack. Based on this, high-precision dressing of the worm gear grinding wheel tooth surface can be achieved by simulating the envelope motion of a single tooth profile of the feed rack. (Refer to...) Figure 2 Adjusting the wheel profile equation: ,in To adjust the pitch circle radius of the wheel, To adjust the wheel cross-section forming parameters, Represents the cosine function. Represents the sine function. Indicates radians, This represents the equation for the modified wheel profile. Pick The left face is represented by the time symbol. The time indicates the right-hand surface. Indicates the normal pressure angle. Indicates the normal modulus; The relative motion relationship between the dressing wheel and the worm grinding wheel is used to construct a spatial coordinate transformation matrix, and then the tooth surface equation of the worm grinding wheel can be derived by using the envelope method. in, The surface equation representing the grinding wheel worm gear is as follows: Pick The left face is represented by the time symbol. The time indicates the right-hand side. Indicates that the dressing wheel is in coordinate system to Transformation matrix of coordinate system express coordinate system to Transformation matrix of coordinate system This indicates the center distance between the dressing wheel and the worm wheel. This indicates the lead angle of the worm gear grinding wheel. This indicates the angle by which the dressing wheel rotates around the worm wheel. Indicates the initial offset , Indicates the worm gear grinding wheel head spacing, specifically , Total number of worm grinding wheels For the normal module of the worm gear grinding wheel, Indicates the first of the worm gear grinding wheel One spiral head.

[0015] The thickened gear tooth surface is created by the worm grinding wheel tooth surface through an envelope motion. This envelope motion system includes the coordinated motion of the worm grinding wheel and the gear: the worm grinding wheel rotates around the B-axis at a set speed, while simultaneously moving along the X and Z axes; the gear, according to the transmission ratio, maintains a meshing relationship with the worm grinding wheel and rotates continuously around the C-axis. (Reference) Figure 3 .

[0016] Establish the processing transformation matrix containing vibration displacement: The vibration displacement is expressed as: in, The numbers represent the indexes of the vibration displacement functions along the principal axes X, Y, and Z. Let X and Z represent the total number of vibration displacement functions along the principal axes X, Y, and Z, respectively. , , These represent the vibration displacement functions along the principal axes X, Y, and Z, respectively. , , These represent the amplitudes of the vibration displacement functions along the principal axes X, Y, and Z, respectively. , , These represent the frequencies of the vibration displacement functions along the principal axes X, Y, and Z, respectively. Indicates processing time. , , Let X, Y, and Z represent the initial phases of the vibration displacement functions along the principal axes, respectively. The processing transformation matrix containing vibration displacement is as follows: in, The rotation angle of the worm gear grinding wheel. For installation angle, For gear rotation angle, Indicates the machining cone angle. This is the axial feed rate of the worm gear grinding wheel. and These represent the center distances in the horizontal and vertical directions of the gear and worm grinding wheel, respectively, as expressed in the following expressions: in, Indicates the pitch circle radius of the gear. Indicates the pitch circle radius of the worm grinding wheel. This indicates the lead angle of the worm gear grinding wheel. This is the axial feed rate of the worm gear grinding wheel. Indicates the nominal helix angle and machining taper angle of the gear. The expression is as follows: in, The nominal taper angle of a gear is used to represent the gear's nominal cone angle. During grinding, the B-axis and Z-axis movements of the machine tool are independent of each other. The relationship between the B-axis and Z-axis can be expressed using the gear rotation angle. Represented as: in, Indicates the number of teeth on a gear. This indicates the total number of threads on the worm gear grinding wheel. The specific expression for the auxiliary angle is as follows: in, Representing the arctangent trigonometric function, the position vector and normal vector of the grinding wheel tooth surface in the gear coordinate system are: in, This represents the position vector of the grinding wheel tooth surface in the gear coordinate system. This represents the normal vector of the grinding wheel tooth surface in the gear coordinate system. This represents the surface equation of the grinding wheel worm gear. This represents the normal vector of the tooth surface of the grinding wheel worm. They are respectively The upper left triangular submatrix.

[0017] To determine the meshing point between the gear and the worm wheel, specifically, based on the meshing principle of continuous generating grinding of gears, and considering the dynamic relative motion between the worm wheel and the gear being processed during the grinding process, and since the product of the relative velocity at the meshing point and the normal vector of the common tangent plane is zero, a numerical iterative algorithm is used to solve the equation, obtaining the gear tooth surface enveloped by the meshing point: in, This represents the product of the velocity vector and the normal vector of the relative movement between the worm gear grinding wheel and the gear tooth surfaces at the meshing point. This represents the product of the velocity vector and the normal vector of the relative rotation between the worm gear grinding wheel and the gear tooth surfaces at the meshing point. The equation representing the gear tooth surface enveloped by the meshing point; S2: Establish the equation of the theoretical gear tooth surface and discretize the theoretical tooth surface to obtain discrete points uniformly distributed on the theoretical tooth surface; Select a specific tooth surface and establish the corresponding theoretical tooth surface equation: (j=l,r) in, The theoretical tooth surface equation representing the tooth surface. j Pick l Indicates the left tooth surface. j Pick r Indicates the right tooth surface. Indicates the pitch. It is the radius of the base circle. It is the unfolding angle. It is the dynamic initial angle of the involute. To ensure proper meshing between the grinding wheel, worm gear, and gear teeth, the rotation angle of the tooth surface is crucial, especially for the thickened gear tooth surface, which is generated by the helical upward motion of the involute. This is because the involute at the gear's end face moves axially... At that time, the dynamic initial angle of the involute The calculation is as follows: The left tooth surface is marked with a "+", and the right tooth surface is marked with a "-". Let be the pitch circle radius of the gear. Indicates the end face pressure angle. It is the radius of the base circle. Indicates the nominal helix angle of the gear. Indicates the nominal cone angle of the gear. Indicates the normal pressure angle; S3: Calculate the normal distance between discrete points on the theoretical tooth surface and the grinding wheel profile at each meshing point position, and continuously update it, retaining the minimum normal distance between each discrete point and the grinding wheel profile. Map the above discrete points to a three-dimensional coordinate system with the meshing line as the abscissa, the tooth width position as the ordinate, and the normal distance as the height coordinate, and fit it into a three-dimensional surface; The theoretical tooth surface obtained from equation modeling consists of a mesh and cannot be directly used for calculation. Therefore, further "discretization" of the mesh is required to form a series of discrete points uniformly distributed on the tooth surface. Using the boundary coordinates of the mesh elements as constraints, a parametric mapping method (uniformly dividing the parameter domain of the mesh elements and then substituting it into the tooth surface equation to solve for the corresponding spatial coordinates) is used to generate an equal number of discrete points with consistent spacing within each element. Figure 4 .

[0018] At any given moment, when the worm tooth surface and the gear tooth surface make point contact, the discrete points on the theoretical tooth surface will generate a normal distance with the worm tooth surface. This normal distance is the residual height after grinding. The normal distance between these discrete points and the worm tooth surface may change with the change of the meshing point, and its minimum value is the final residual height obtained after grinding.

[0019] The mathematical expression for residual calculation is: in, K is the unit normal vector of the theoretical tooth surface, with a magnitude of 1, therefore K min (i.e., K) min The value of (=min{K}) is the obtained normal residual height. In essence .

[0020] The calculation process for the normal residual height between the theoretical tooth surface and the actual tooth surface is as follows: (Refer to...) Figure 5 : The waviness is obtained by plotting the unfolded length L of the line of engagement as the x-axis, the tooth width d as the y-axis, and the residual value K of each point on the actual tooth surface as the height coordinate. (Refer to...) Figure 6 .

[0021] S4: Perform a two-dimensional Fourier transform on the fitted surface to obtain a waviness surface that can be characterized by two-dimensional trigonometric functions. Fourier decomposition was performed by sampling along the waviness x (meshing line unfolded length L) and y (tooth width position d) directions respectively, and referenced. Figure 7 Finally, the ripple characterization function composed of two-dimensional trigonometric functions is obtained: Where M is the number of sampling points in the x-direction and N is the number of sampling points in the y-direction, the actual spatial step size is: in The sampling length in the x-direction. The sampling length is in the y-direction.

[0022] The spatial frequencies in the x and y directions are respectively , ; No. , The actual physical coordinates of the sampling point are ; Indicates the first OK ripple amplitude of sampling points .

[0023] After performing a two-dimensional Fourier transform on the above waviness, retaining the DC component and the two components with the largest amplitude, the following waviness was obtained (reference). Figure 8 and characterization parameters: Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for characterizing the waviness of ground tooth surfaces, characterized in that: Includes the following steps: S1: Construct a continuous generating grinding mathematical model that includes vibration parameters, and solve to determine the meshing point between the gear and the worm wheel; S2: Establish the equation of the theoretical gear tooth surface and discretize the theoretical tooth surface to obtain discrete points uniformly distributed on the theoretical tooth surface; S3: Calculate the normal distance between discrete points on the theoretical tooth surface and the grinding wheel profile at each meshing point position, and continuously update it, retaining the minimum normal distance between each discrete point and the grinding wheel profile; map the above discrete points to a three-dimensional coordinate system with the meshing line as the abscissa, the tooth width position as the ordinate, and the normal distance as the height coordinate, and fit it into a three-dimensional surface. S4: Perform a two-dimensional Fourier transform on the fitted surface to obtain a waviness surface that can be characterized by two-dimensional trigonometric functions.

2. The method for characterizing the waviness of ground tooth surfaces according to claim 1, characterized in that: In step S1, the meshing point between the gear and the worm wheel is determined by solving a numerical iterative algorithm based on the meshing principle of continuous gear generating grinding, combined with the dynamic relative motion relationship between the worm wheel and the gear to be processed during the grinding process, and based on the fact that the product of the relative velocity at the meshing point and the normal vector of the common tangent plane is zero, to obtain the gear tooth surface enveloped by the meshing point.

3. The method for characterizing the waviness of ground tooth surfaces according to claim 2, characterized in that: The specific expression for the equation establishing the theoretical gear tooth surface in S2 is as follows: in, Indicates tooth surface The theoretical tooth surface equation, ,when The time indicates the left tooth surface. The time indicates the right tooth surface. Represents the cosine function. Represents the sine function. Indicates the pitch. Indicates the development angle. This represents the dynamic initial angle of the involute. This indicates the angle of rotation of the tooth surface when the grinding wheel, worm gear, and gear tooth surfaces are correctly meshed before machining. This represents the radius of the base circle.

4. The method for characterizing the waviness of ground tooth surfaces according to claim 3, characterized in that: The radius of the base circle The specific expression is as follows: in, Represents the tangent function. Represents the cosine function. Represents the sine function. Indicates the normal pressure angle. Indicates the nominal helix angle of the gear. Indicates the nominal cone angle of the gear. Let be the pitch circle radius of the gear.

5. The method for characterizing the waviness of ground tooth surfaces according to claim 3, characterized in that: The dynamic initial angle of the involute The specific expression is as follows: in, Represents the tangent function. Represents the cosine function. Represents the sine function. Indicates the number of teeth on a gear. Indicates the end face pressure angle. This indicates the length of axial movement of the involute curve on the end face of the gear.

6. The method for characterizing the waviness of ground tooth surfaces according to claim 1, characterized in that: The specific steps of S4 are as follows: sample along the x and y directions of waviness and perform Fourier decomposition, as shown in the following expressions: in, Represents a waviness surface. These represent the x-direction and the y-direction, respectively.

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